How do you find the domain and range of # y = -sqrt(x+6)+7 #?

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Answer 1 · 2018-06-19T05:34:32

The domain is #x in [-6,+oo]#. The range is #y in (-oo,7]#

The function is

#y=-sqrt(x+6)+7#

What's under the square root sign must be #>=0#

Therefore,

#x+6>=0#

#=>#, #x>=-6#

The domain is #x in [-6,+oo]#

When #x=-6#

#y=-sqrt(-6+6)+7=0+7=7#

And when #x-> +oo#

#y->(-sqrt(+oo+6)+7)=-oo#

The range is #y in (-oo,7]#

graph{-sqrt(x+6)+7 [-32.17, 71.9, -28.34, 23.65]}